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Full text of "Men Of Mathematics"

THE LAST UNIVERSALIST
tion, are not contradicted by those who would reverse the
ngtires. Both are right; one man remembers the drudgery while
another forgets it all in the thrill of apparently sudden discovery,
but both, when they analyse their impressions, admit that
without drudgery and a flash of 'inspiration" discoveries are not
made. If drudgery alone sufficed, how is it that many gluttons
for hard work who seem to know everything about some branch
of science, while excellent critics and commentators, never
themselves make even a small discovery? On the other hand,
those who believe in 'inspiration' as the sole factor in discovery
or invention - scientific or literary - may find it instructive to
look at an early draft of any of Shelley's 'completely sponta-
neous' poems (so far as these have been preserved and repro-
duced), or the successive versions of any of the greater novels
that Balzac inflicted on his maddened printer.
Poincare stated his views on mathematical discovery in an
essay first published in 1908 and reproduced hi his Science et
llethode. The genesis of mathematical discovery, he says, is a
problem which should interest psychologists intensely, for it is
the activity in which the human mind seems to borrow least
from the external world, and by understanding the process of
mathematical thinking <we may hope to reach what is most
essential in the human mind.
How does it happen, Poincare* asks, that there are persons
who do not understand mathematics? 'This should surprise us,
or rather it would surprise us if we were not so accustomed to
it.* If mathematics is based only on the rules of logic, sneh as all
normal minds accept, and which only a lunatic would deny
(according to Poincare), how is it that so many are mathemati-
cally impermeable? To which it may be answered that no
exhaustive set of experiments substantiating mathematical
incompetence as the normal human mode has yet been pub-
lished. *And further', he asks, 'how is error possible in mathe-
matics?' Ask Alexander Pope: *To err is human% which is as
unsatisfactory a solution as any other. The chemistry of the
digestive system may have something to do with it, but Pom-
care* prefers a more subtle explanation - one which could not be
tested by feeding the 'vile body* hasheesh and alcohol.
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